Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem asks us to find the equation of a plane that contains two given parallel lines. The para...
Plane GeometryVectorsCross ProductParametric EquationsLines in 3DEquation of a Plane
2025/4/13
The problem asks to find the symmetric equations of the line of intersection of two given planes. Th...
LinesPlanesVector AlgebraCross ProductLinear Equations
2025/4/13
The problem requires us to write an algorithm (in pseudocode) that calculates the area of a circle. ...
AreaCircleAlgorithmPseudocode
2025/4/13
The problem asks us to find the parametric and symmetric equations of a line that passes through a g...
Lines in 3DParametric EquationsSymmetric EquationsVectors
2025/4/13
Find the angle at point $K$. Given that the angle at point $M$ is $60^\circ$ and the angle at point ...
AnglesTrianglesParallel Lines
2025/4/12
We are given a line segment $XY$ with coordinates $X(-8, -12)$ and $Y(p, q)$. The midpoint of $XY$ i...
Midpoint FormulaCoordinate GeometryLine Segment
2025/4/11
In the circle $ABCDE$, $EC$ is a diameter. Given that $\angle ABC = 158^{\circ}$, find $\angle ADE$.
CirclesCyclic QuadrilateralsInscribed AnglesAngles in a Circle
2025/4/11
Given the equation of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $a \neq b$, we need ...
EllipseTangentsLocusCoordinate Geometry
2025/4/11
We are given a cone with base radius $r = 8$ cm and height $h = 11$ cm. We need to calculate the cur...
ConeSurface AreaPythagorean TheoremThree-dimensional Geometry
2025/4/11
$PQRS$ is a cyclic quadrilateral. We are given the measures of its angles in terms of $x$ and $y$. W...
Cyclic QuadrilateralAnglesLinear EquationsSolving Equations
2025/4/11